MCQ
The value of $c$ for which the equation $ax^2+ 2bx + c = 0$ has equal roots is :
- ✓$\frac{\text{b}^2}{\text{a}}$
- B$\frac{\text{b}^2}{4\text{a}}$
- C$\frac{\text{a}^2}{\text{b}}$
- D$\frac{\text{a}^2}{4\text{b}}$
✓
Answer
Correct option: A.
$\frac{\text{b}^2}{\text{a}}$
$ \Rightarrow a x^2+2 b x+c=0 $
$ \Rightarrow D=b^2-4 a c $
$ \Rightarrow D=(2 b)^2-4 \times a \times c $
$ \Rightarrow D=4 b^2-4 a c$
Roots are equal
$ \Rightarrow D=0 $
$ \Rightarrow 4 b^2-4 a c=0 $
$ \Rightarrow 4 a c=4 b^2 $
$\Rightarrow\text{c}=\frac{4\text{b}^2}{4\text{a}}$
$\Rightarrow\text{c}=\frac{\text{b}^2}{\text{a}}$
$ \Rightarrow D=b^2-4 a c $
$ \Rightarrow D=(2 b)^2-4 \times a \times c $
$ \Rightarrow D=4 b^2-4 a c$
Roots are equal
$ \Rightarrow D=0 $
$ \Rightarrow 4 b^2-4 a c=0 $
$ \Rightarrow 4 a c=4 b^2 $
$\Rightarrow\text{c}=\frac{4\text{b}^2}{4\text{a}}$
$\Rightarrow\text{c}=\frac{\text{b}^2}{\text{a}}$
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